Clark's 10-over return gave south conference table-toppers Hampshire a home semi-final against Warwickshire a week on Wednesday.
Former England batsman Mark Ramprakash won the toss and elected to bat. But Clark removed the Surrey top three while Ramprakash himself was bowled for nought by all-rounder Dimitri Mascarenhas.
At one stage Surrey were 32 for six before a stand of 122 between ex-England duo Rikki Clarke (55) and Chris Schofield (75 not out) helped them recover to 181 all out.
Hampshire captain and former Australia leg-spinner Shane Warne took one for 46 from his 10 overs.
Hampshire, who then saw former England batsman John Crawley make 55, were cruising at 165 for three before a flurry of late wickets gave Surrey the merest glimmer of hope. But a no-ball from Australia seamer Matthew Nicholson sealed the south coast county's victory.
Somerset captain Justin Langer made 82 but couldn't prevent Essex booking their last four place with a seven-wicket win at Chelmsford.
Langer was left playing a lone hand as Pakistan leg-spinner Danish Kaneria took five for 32 in Somerset's 193 all out.
Opening batsman Mark Pettini made a rapid 87 off 79 balls in reply and England one-day international all-rounder Ravi Bopara saw Essex home with an unbeaten 51.
Warwickshire secured second spot in the North Conference behind a Durham side already through to the semi-finals with a rain-affected win by 39 runs against the north-east team at Edgbaston under the Duckworth-Lewis method.
Hundreds from Tim Ambrose (135) and Jonathan Trott (107 not out) saw the Bears to 314 for five. Durham were 77 for three in reply when rain stopped play but enough cricket had taken place for Warwickshire to be declared the winners.
Surrey 181 all out in 49.5 overs (Chris Schofield 75 n o, Rikki Clarke 55; Stuart Clark 6 for 27, Warne 1 for 46) lost to Hampshire 182 for 7 in 48.2 overs (Crawley 55, Carberry 36, Benham 28, Ervine 25; Nicholson 2 for 27, Rikki Clarke 2 for 40, Doshi 1 for 26).
Somerset 193 all out 49.4 overs (Justin Langer 82; Danish Kaneria 5 for 32, Saggers 3 for 36) lost to Essex 194 for 3 in 34.2 overs (Pettini 87, Ravinder Bopara 51 n o; Blackwell 2 for 59).
Warwickshire 314 for 5 in 50 overs (Ambrose 135, Trott 107, Troughton 37; Killeen 2 for 49) VsDurham 77 for 3 in 16.2 overs (Di Venuto 38, Smith 23; Daggett 2 for 39). Result: Warwicks beat Durham by 39 runs under D/L method.